Answer:
Yes; [tex](7x^3+9b)(7x^3-9b)[/tex]
Step-by-step explanation:
A difference of squares is basically where you have two terms that can both be written in the form of [tex]k^2[/tex] and one is subtracting the other.
Here, the first term is [tex]49x^6[/tex] . We see that if we square root this, we will come out with the clean number: [tex]7x^3[/tex] (because [tex]7x^3*7x^3=49x^6[/tex]).
The second term is [tex]81b^2[/tex] . Again, we see that if we square root this, we will get the clean result: [tex]9b[/tex] (because [tex]9b*9b=81b^2[/tex]).
So, they are indeed both squares; thus, this is a difference of squares.
To factor it, we remember the formula for factoring [tex]a^2-b^2[/tex]: [tex]a^2-b^2=(a+b)(a-b)[/tex]
In this case, a = 7x^3 and b = 9b, so:
[tex]49x^6-81b^2=(7x^3+9b)(7x^3-9b)[/tex], and that's the answer.
Hope that helps!
